ePSXe 1.8.0 runs cue files perfectly they do need to be in the same folder as the bin and bin is not to be renamed as that will make it not work
Open the cue file with notepad though and make sure it is looking for the correct file (cue files are just text files anyway but they tell whatever reads them what is in the bin or img file including CDDA tacks)
offscreen drawing is only in the 3D video plugins
It is very possible by what you have said, that the issue is just to do with you not using the cue file as that game does have a CDDA track and with you just loading the bin file directly you are resulting in the game not having CDDA and some games will just not run without it
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